Adding a 5th slot wouldn't change anything. I played all three roles in WoW, where the group is 1 tank, 1 heal, 3 DPS, and the queue times were exactly like they are in FF14. Tanks pop instantly, healers almost instantly, DPS wait 5-20 minutes.

Nobody wants to tank/heal and take abuse from the playerbase, which they will, when things go wrong, which they always do. That's why DPS queues always suck.

If you don't like DPS queue times, then play a tank or a healer. And if you won't be a tank or healer, ask yourself why not. The answer is likely the same or very similar for the vast majority of the playerbase.